**NCERT Solutions for Class 8 Chapter 12 Exponents and Powers** will help students aiming for high marks in their examination. Refer to the NCERT Class 8 Mathematics Exercise Solutions and practise the questions and answers based on the CBSE curriculum to understand the concepts covered in the chapter. We can say that an expression which represents repeated multiplication of the same factor is called a power. For example, in case of 4^{2}, the number 4 is called the base, and the number 2 is the exponent. An Exponent corresponds to the number of times the base is utilized as a factor in an expression.

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## Exercise 12.1 Page No: 197

**1. Evaluate:**

**(i) 3 ^{-2 }(ii) (-4)^{-2 } (iii) (1/2)^{-5} **

**Solution:**

(i) 3^{-2 }= (1/3)^{2}

= 1/9

(ii) **(-4) ^{-2 } = (1/-4)^{2}**

= 1/16

(iii) **(1/2) ^{-5} = (2/1)^{5}**

= 2^{5}

= 32

**2. Simplify and express the result in power notation with positive exponent:**

**(i) (-4) ^{4 }÷(-4)^{8} **

**(ii) (1/2 ^{3})^{2} **

**(iii) -(3) ^{4}×(5/3)^{4} **

**(iv) (3 ^{-7}÷3^{-10})×3^{-5} **

**(v) 2 ^{-3}×(-7)^{-3}**

**Solution:**

(i)

= (-4)^{5}/(-4)^{8}

= (-4)^{5-8 }

= 1/(-4)^{3}

(ii) **(1/2 ^{3})^{2} **

= 1^{2}/(2^{3})^{2}

= 1/2^{3×2} = 1/2^{6}

(iii) **-(3) ^{4}×(5/3)^{4} **

= (-1)^{4}×3^{4}×(5^{4}/3^{4} )

= 3^{(4-4)}×5^{4}

= 3^{0}×5^{4} = 5^{4}

(iv)** **

= (3^{-7}/3^{-10})× 3^{-5}

= 3^{-7 – (-10) }× 3^{-5 }

= 3^{(-7+10)}×3^{-5}

= 3^{3}×3^{-5}

= 3^{(3+-5)}

= 3^{-2}

=1/3^{2 }

(v) 2^{-3}×(-7)^{ – 3}

= (2×-7)^{-3}

(Because a^{m}×b^{m} = (ab)^{m})

= 1/(2×-7)^{3 }

= 1/(-14)^{3}

**3. Find the value of :**

**(i) (3 ^{0}+4^{-1})×2^{2}**

**(ii) (2 ^{-1}×4^{-1})÷2^{ – 2}**

**(iii) (1/2) ^{-2}+(1/3)^{-2}+(1/4)^{-2 }**

**(iv) (3 ^{-1}+4^{-1}+5^{-1})^{0}**

**(v) {(-2/3) ^{-2}}^{2}**

**Solution:**

(i)(3^{0}+4^{– 1})×2^{2} = (1+(1/4))×2^{2}

= ((4+1)/4 )×2^{2}

= (5/4)×2^{2}

= (5/2^{2})×2^{2}

= 5×2^{(2-2)}

= 5×2^{0}

= 5×1 = 5

(ii)(2^{-1}×4^{-1})÷2^{-2}

= [(1/2)×(1/4)] ÷(1/4)

= (1/2×1/2^{2} )÷ 1/4

= 1/2^{3}÷1/4

= (1/8)×(4)

= 1/2

(iii) **(1/2) ^{-2}+(1/3)^{-2}+(1/4)^{-2 }**

= (2^{-1})^{-2}+(3^{-1})^{-2}+(4^{-1})^{-2}

= 2^{(-1×-2)}+3^{(-1×-2)}+4^{(-1×-2)}

= 2^{2}+3^{2}+4^{2}

= 4+9+16

=29

(iv) (3^{-1}+4^{-1}+5^{-1})^{0}

= 1

(v) **{(-2/3) ^{-2}}^{2} = (-2/3)^{-2×2}**

= (-2/3)^{-4}

= (-3/2)^{4}

= 81/16

**4. Evaluate**

**(i) (8 ^{-1}×5^{3})/2^{-4}**

**(ii) (5 ^{-1}×2^{-2})×6^{-1} **

**Solution:**

(i) (8^{-1}×5^{3})/2^{-4}

=

= 2×125 = 250

**(ii)** **(5 ^{-1}×2^{-2})×6^{-1} **

= (1/10)×1/6

= 1/60

**5. Find the value of m for which 5^{m }÷ 5^{-3} = 5^{5}**

**Solution:**

5* ^{m}* ÷ 5

^{-3}= 5

^{5}

5^{(m-(-3) )} = 5^{5}

5^{m+3} =5^{5}

Comparing exponents both sides, we get

m+3 = 5

m = 5-3

m = 2

**6. Evaluate**

**(i) **

**(ii) **

**Solution:**

**(i)**

= 3-4

= -1

**(ii)**

=

=

=

= 512/125

**7. Simplify.**

**(i) **

**(ii) **

Solution:

**(i)**

=

=

**(ii)**

=

=

=

=

= 1×1×3125

= 3125

## Exercise 12.2 Page No: 200

**1. Express the following numbers in standard form.**

**(i) 0.0000000000085**

** (ii) 0.00000000000942**

** (iii) 6020000000000000**

** (iv) 0.00000000837**

** (v) 31860000000**

**Solution:**

(i) 0.0000000000085 = 0.0000000000085×(10^{12}/10^{12}) = 8.5 ×10^{-12}

(ii) 0.00000000000942 = 0.00000000000942×(10^{12}/10^{12}) = 9.42×10^{-12}

(iii) 6020000000000000 = 6020000000000000×(10^{15}/10^{15}) = 6.02×10^{15}

(iv) 0.00000000837 = 0.00000000837×(10^{9}/10^{9}) = 8.37×10^{-9}

(v) 31860000000 = 31860000000×(10^{10}/10^{10}) = 3.186×10^{10}

**2.Express the following numbers in usual form.**

**(i) 3.02×10 ^{-6}**

**(ii) 4.5×10 ^{4}**

**(iii)3×10 ^{-8}**

**(iv)1.0001×10 ^{9}**

**(v) 5.8×10 ^{12}**

**(vi)3.61492×10 ^{6}**

Solution:

(i) 3.02**×**10^{-6} = 3.02/10^{6} = 0 .00000302

(ii) 4.5**×**10^{4} = 4.5**×**10000 = 45000

(iii) 3**×**10^{-8} = 3/10^{8} = 0.00000003

(iv) 1.0001**×**10^{9} = 1000100000

(v) 5.8**×**10^{12} = 5.8**×**1000000000000 = 5800000000000

(vi) 3.61492**×**10^{6 }= 3.61492**×**1000000 = 3614920

**3. Express the number appearing in the following statements in standard form.**

**(i) 1 micron is equal to 1/1000000 m. (ii) Charge of an electron is 0.000, 000, 000, 000, 000, 000, 16 coulomb. (iii) Size of bacteria is 0.0000005 m (iv) Size of a plant cell is 0.00001275 m (v) Thickness of a thick paper is 0.07 mm**

**Solution :**

(i) 1 micron = 1/1000000

= 1/10^{6}

= 1×10^{-6}

(ii) Charge of an electron is 0.00000000000000000016 coulombs.

= 0.00000000000000000016**×**10^{19}/10^{19}

= 1.6**×**10^{-19 }coulomb

(iii) Size of bacteria = 0.0000005

= 5/10000000 = 5/10^{7} = 5×10^{-7} m

(iv) Size of a plant cell is 0.00001275 m

= 0.00001275×10^{5}/10^{5}

= 1.275×10^{-5}m

(v) Thickness of a thick paper = 0.07 mm

0.07 mm = 7/100 mm = 7/10^{2} = 7×10^{-2} mm

**4. In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack?**

Solution:

Thickness of one book = 20 mm

Thickness of 5 books = 20×5 = 100 mm

Thickness of one paper = 0.016 mm

Thickness of 5 papers = 0.016×5 = 0.08 mm

Total thickness of a stack = 100+0.08 = 100.08 mm

= 100.08×10^{2}/10^{2} mm

mm

### NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers

These NCERT solutions help students to gain a better understanding of the topic and learn the concepts with ease. This learning material is designed by subject experts as per the CBSE latest syllabus prescribed by the board. In Class 8 CBSE chapter 12 of Maths, students will learn about how to write large numbers more conveniently using exponents and powers, express numbers in standard form, dealing with negative exponents, various laws of exponents and many more.**NCERT Solutions For Class 8 Maths Chapter 12 Exercises:**

Get detailed solution for all the questions listed under below exercises:

Exercise 12.1 Solutions : 7 Questions (Short answers)

Exercise 12.2 Solutions : 4 Questions (Short answers)

### NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers

NCERT Solutions for Class 8 Maths Chapter 12, Exponents and Powers is about the law of exponents, powers and their applications.**The main topics covered in this chapter include:**

Exercise | Topic |

12.1 | Introduction |

12.2 | Powers with Negative Exponents |

12.3 | Laws of Exponents |

12.4 | Use of Exponents to Express Small Numbers in Standard Form |

### Key Features of NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers

- Easy and simple language used.
- NCERT Solutions will help in boosting the confidence level among students.
- Subject experts have consolidated all exercises questions at one place which could feature in your exam.
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